2 stat problems

1) The average size of insurance claims processed by Good-Wish Insurance Company for the month of August is $710. If you assume that the population of insurance claims is not symmetric, at least what percent of claims is within 1.6 standard deviations of the mean? (Enter your answer to two decimal places) --> I have no clue how to approach this problem because it says that it's not symmetric. I figured I'd try Chebyshev's inequality and say that the answer was 50% because sqrt(2) is the closest thing to 1.6 that is available as to my knowledge, and I tried and that wasn't the right answer. Then I figured I'd use a symmetric and use the Z-table, but that wasn't successful either.

2) What is the standard deviation of the X, the number of students who may have to stand? --> for this I just need an answer, not a solution (but if you want provide one.

The probability distribution is, once again, given below.

X 0 1 2 3 4 5
P(X) .6 .2 .1 .05 .03 .02

Report your answer to FOUR decimal places.

I found that the mean is .77, but when i try to subtract values from the mean and divide by n and sqrt it doesn't work out properly.